### np-complete

#### Knapsack for each weight having multiple values - Is it possible to solve?

I have a 0/1 minimization Knapsack problem with a sum equality constraint. However, more interestingly, my weights can take values between 0:15. My question is, can I really solve this problem in polynomial time and, if yes, how? By the way, I have n=100 items, all of whose weights (w_i) can be between 0 and 15. In addition, my values (v_i) change for each item when the weight changes in the given range. Also my equality value is 212.

### Related Links

NP-complete or NP-hard?

Why using linear integer programming (ILP) though it is NP-Complete?

Prove NP-Completeness of generating 2 shortest routes over given edge grouping constraints?

Reduction to Clique prob

Approximation Algorithm between two NP compete problems

Is it possible to find the probability to a solution of NP-complete problems?

Knapsack for each weight having multiple values - Is it possible to solve?

Reduction from Maximum independent set to Dominating set to prove the Dominating set is NP-complete

How I can prove that 2-CNF is not NP-complete?

When NP complete becomes NP hard

Can it be proven no polynomial algorithm exists for an NP-Complete prob.?

Effect of number base when proving NP completeness of numerical problems

How to reduce 3COLOR to 3SAT?

proof NP-complete

Proof that Dominating Set is NP-Complete

Is this an NP problem?